*3.5. Experimental Verification*

Experiments were fulfilled on H630 rolling mills and Figure 15a–c shows respectively the rolling mill, rolling die, and a picture of the infrared thermometer. Stepped shaft products from a traditional billet and from a billet with a variable cone angle are shown in Figure 16. Figure 17 is the comparison between simulation and experimental results. Table 2 compares the statistical data of the simulation and experimental concaves.

**Figure 15.** Diagram of the rolling site: (**a**) the H630 type rolling mill; (**b**) the cross-wedge rolling die; (**c**) heating device.

**Figure 16.** Billets and rolled products: (**a**) comparison of billets; (**b**) lateral comparison of rolled products; (**c**) axial comparison of rolled products.

**Figure 17.** Comparison of Simulation (**a**,**c**) and Experimental (**b**,**d**) rolling effects of stepped shafts: (**a**) simulation results of rolling by a traditional billet; (**b**) experiment results of rolling by traditional billet; (**c**) simulation results of rolling by a billet with a variable cone angle; (**d**) experiment results of rolling by a billet with a variable cone angle.

**Table 2.** Concave depth statistics of finite element simulation and experimental results of stepped shaft by cross-wedge rolling.


Through comparison, the simulation and experimental results are basically consistent. Specifically, the simulated concave depth using traditional billet is 25.44 mm, and in practical rolling, the figure is 24.95 mm, with the error ratio at 1.9%. By means of billets with a variable cone angle, the simulated depth is 1.93 mm, and the practical result is 1.85 mm, with the error at 4%. The depth of concave of the rolling pieces using a cone-shaped billet is about 92.5% smaller than those using traditional billets, and the utilization rate is 14% higher comparatively. Based on the results of finite element simulation and rolling experiment, the rolling of stepped shafts using billets with a variable cone angle has the outstanding impact on resolving end concave problems and enhancing the utilization rate of the material.

The billet end can be preformed to a variable cone angle shape before cross-wedge rolling by the hot roller shearing equipment [21,22] developed by our research group, and the near-net forming technology for stepped shaft by cross-wedge rolling based on variable cone angle billets has also reached the industrial application level.

#### **4. Conclusions**


influence of the total cone section length **m**. The depth of concave will firstly decrease and then increase with the increasing of the cone angle α and of the first cone section length **n**, and will decrease with the increasing of the total cone section length **m**.

3. Through comparison, the error ratio between the experimental and simulation results of rolling stepped shafts using billets with a variable cone angle is lower than 5%. It means that the results of finite element simulation are reliable, and can reflect the changes of shaping of the rolling piece during practical production.

**Author Contributions:** S.H. designed the experiment scheme, carried out the cross wedge rolling experiment and wrote the manuscript. X.S. participated in the design of the experiment scheme, the cross wedge rolling experiment, the writing and the revision of the manuscript. C.S. participated in the revision of the manuscript and cross wedge rolling experiment.

**Funding:** This research was funded by K.C. Wong Education Foundation, Hong Kong, the National Natural Science Foundation of China [grant number 51475247], and The Natural Science Foundation of Zhejiang [grant number LZ17E050001].

**Conflicts of Interest:** The authors declare no conflicts of interest.
